The idea that dogs will try to "dominate" you unless you maintain your role as "alpha," and that all dog behavior problems arise from this struggle for "dominance," is based on bad science.
There are novels written about this but here is a super-condensed version .
The "dominance" theory started with observations of the behavior ants (yup, ants) and was erroneously applied to all groups of animals. The concept of alpha was added after studies of captive wolves in the 1970's (wolves who had no association with one another that were thrown together, thus creating an unstable social structure) were seen to fight for their "rank" within the group. These then, in turn, were applied to dog social interaction, and despite the body of research that has since been done with wolves, as well as feral and domestic dogs that disproves these assumptions (that feral dogs form packs like wolves, that you must always eat before your dog to establish "alpha", that struggles for power in a wolf pack are frequent and violent, etc.) they continue to persist. Even at the behest of the scientists who performed the original research.